Well, it is even easier if there is no need to send a wishlist to some other recipient apart from the store owner and the customer. Ecwid by default sends email notifications about placed orders (in your case, wishlists) to the store admin and to a customer. Moreover, the store admin will be able to see the placed order in their control panel. With these requirements, no extra coding needed - Ecwid already supports everything you asked for.

Perhaps, you will also need to change other buttons and text labels (Shopping cart -> Wishlist, Place order -> Send wishlist etc.) . That can be done by means of custom translations as described in this article: http://goo.gl/gT7eO .